पृष्ठम्:Ganita Sara Sangraha - Sanskrit.djvu/३५१

The rule for arriving at (the value of) the wages corresponding to the various stages (over which varying numbers of persons carry a given weight) :- 230. The distances (travelled over by the various numbers of men) are (respectively) to be divided by the numbers of the men that are (doing the work of carrying) there. The quotients (so obtained) have to be combined so that the first (of them is taken at first separately and then) has (1, 2, and 3, etc, of) the following (quotients) added to it (These quantities so resulting are to be respectively) multiplied by the numbers of the men that turn away (from the journey at the various stages Then) by adopting in relation to these resulting products) the process of proportionate distribution (praksēpaka), the wages (due to the men leaving at the different stages) may be found out. An example in illustration thereof. 231-232 Twenty men have to carry a palanquin over (a distance of) 2 yojanas, and 720 dinaras form their wages. T'wo men stop away after going over two krosas; after going over two (more) krösas, three others (stop away): after going over half of the remaining distance, five men stop away. What wages do they (the various bearers) obtain ? The rule for arriving at (the value the money contents of) a purse which (when added to what is on hand with each of certain persons) becomes a specified multiple (of the sum of what is on hand with the others) :-- 233-235. The quantities obtained by adding one to (each of the specified) multiple numbers (in the problem, and then) 233-235 In the problem given in 236-237, let x, y, z represent the moneys on hand with the three merchants, and u the money in the purse. Then u+= a (y + 2)] where a, b, c represent the multiples u+y=b (z+x) given in the problem. u+z= (x+y) J Now u+x+y+z= (a + 1) (y + 2) = (b + 1) (z+x) (c+1) (x+y). 20